Leotards
Sized child small through adult medium. The brand chart is the source of truth.
Three to four leotards is the working set. Chlorinated pools and chalk dust shorten their life.
Grips
Bars only. Level 4 or 5 is when most gyms introduce grips.
Sized by hand width. The gym's coach will help. Do not buy unprompted.
Hair
A small pouch with hair ties, bobby pins, gel, and a small hairbrush. Lives in the bag.